Representation of Dynamical Stimuli in Populations of Threshold Neurons

Many sensory or cognitive events are associated with dynamic current modulations in cortical neurons. This raises an urgent demand for tractable model approaches addressing the merits and limits of potential encoding strategies. Yet, current theoretical approaches addressing the response to mean- and variance-encoded stimuli rarely provide complete response functions for both modes of encoding in the presence of correlated noise. Here, we investigate the neuronal population response to dynamical modifications of the mean or variance of the synaptic bombardment using an alternative threshold model framework. In the variance and mean channel, we provide explicit expressions for the linear and non-linear frequency response functions in the presence of correlated noise and use them to derive population rate response to step-like stimuli. For mean-encoded signals, we find that the complete response function depends only on the temporal width of the input correlation function, but not on other functional specifics. Furthermore, we show that both mean- and variance-encoded signals can relay high-frequency inputs, and in both schemes step-like changes can be detected instantaneously. Finally, we obtain the pairwise spike correlation function and the spike triggered average from the linear mean-evoked response function. These results provide a maximally tractable limiting case that complements and extends previous results obtained in the integrate and fire framework. Author Summary: Sensory stimuli in our environment are represented in the brain as input current changes to neurons. For example, a periodic bar pattern in the visual field leads to periodic current modulations in the visual cortex. Therefore, models describing the ability of neurons to represent incoming stimuli can offer important clues about how sensory stimuli are processed by the brain. As anyone who has used an old-fashioned radio can attest, there is not just one but multiple ways to encode a signal, e.g. the familiar AM and FM channels. But what are the potential encoding channels in the cortex? A signal could modify the neuronal input current in two distinct ways: it could act either on the mean or the variance of the current. Using a minimal model framework, which can reproduce many features of neuronal activity, we find that both encoding schemes could be equally potent in transmitting slow and fast signals. This allows us to describe how input signals of any functional form give rise to collective firing rate changes in populations of neurons.